Graph summarization via node grouping is a popular method to build concise graph representations by grouping nodes from the original graph into supernodes and encoding edges into superedges such that the loss of adjacency information is minimized. Such summaries have immense applications in large-scale graph analytics due to their small size and high query processing efficiency. In this paper, we reformulate the loss minimization problem for summarization into an equivalent integer maximization problem. By initially allowing relaxed (fractional) solutions for integer maximization, we analytically expose the underlying connections to the spectral properties of the adjacency matrix. Consequently, we design an algorithm called SpecSumm that consists of two phases. In the first phase, motivated by spectral graph theory, we apply k-means clustering on the k largest (in magnitude) eigenvectors of the adjacency matrix to assign nodes to supernodes. In the second phase, we propose a greedy heuristic that updates the initial assignment to further improve summary quality. Finally, via extensive experiments on 11 datasets, we show that SpecSumm efficiently produces high-quality summaries compared to state-of-the-art summarization algorithms and scales to graphs with millions of nodes.

Mathematical models have been used to understand the spread patterns of infectious diseases such as Coronavirus Disease 2019 (COVID-19). The transmission component of the models can be modelled in an age-dependent manner via introducing contact matrix for the population, which describes the contact rates between the age groups. Since social contact patterns vary from country to country, we can compare and group the countries using the corresponding contact matrices. In this paper, we present a framework for clustering countries based on their contact matrices with respect to an underlying epidemic model. Since the pipeline is generic and modular, we demonstrate its application in a COVID-19 model from R\"ost et. al. which gives a hint about which countries can be compared in a pandemic situation, when only non-pharmaceutical interventions are available.

Despite the huge advancement in knowledge discovery and data mining techniques, the X-ray diffraction (XRD) analysis process has mostly remained untouched and still involves manual investigation, comparison, and verification. Due to the large volume of XRD samples from high-throughput XRD experiments, it has become impossible for domain scientists to process them manually. Recently, they have started leveraging standard clustering techniques, to reduce the XRD pattern representations requiring manual efforts for labeling and verification. Nevertheless, these standard clustering techniques do not handle problem-specific aspects such as peak shifting, adjacent peaks, background noise, and mixed phases; hence, resulting in incorrect composition-phase diagrams that complicate further steps. Here, we leverage data mining techniques along with domain expertise to handle these issues. In this paper, we introduce an incremental phase mapping approach based on binary peak representations using a new threshold based fuzzy dissimilarity measure. The proposed approach first applies an incremental phase computation algorithm on discrete binary peak representation of XRD samples, followed by hierarchical clustering or manual merging of similar pure phases to obtain the final composition-phase diagram. We evaluate our method on the composition space of two ternary alloy systems- Co-Ni-Ta and Co-Ti-Ta. Our results are verified by domain scientists and closely resembles the manually computed ground-truth composition-phase diagrams. The proposed approach takes us closer towards achieving the goal of complete end-to-end automated XRD analysis.

Minimalist Data Wrangling with Python is envisaged as a student's first introduction to data science, providing a high-level overview as well as discussing key concepts in detail. We explore methods for cleaning data gathered from different sources, transforming, selecting, and extracting features, performing exploratory data analysis and dimensionality reduction, identifying naturally occurring data clusters, modelling patterns in data, comparing data between groups, and reporting the results. This textbook is a non-profit project. Its online and PDF versions are freely available at https://datawranglingpy.gagolewski.com/.

The second class of methods uses graph embedding, Many real-world systems can be represented as graphs where the in particular graph autoencoders. Graph convolutional network different entities are presented by nodes and their interactions by (GCN) based methods such as Graph autoencoders (GAE) [13], variational edges. An important task in studying large datasets is graph clustering. GAE (VGAE) [14], adversarially regularized graph autoencoder While there has been a lot of work on graph clustering using the (ARGA), adversarially regularized variational graph autoencoder connectivity between the nodes, many real-world networks also have (ARVGA) [15] and marginalized graph autoencoder for graph node attributes. Clustering attributed graphs requires joint modeling clustering (MGAE) [16] have demonstrated state-of-the-art performance of graph structure and node attributes. Recent work has focused on on several attributed graph clustering tasks. These methods graph convolutional networks and graph convolutional filters to combine directly use GCN as a feature extractor, where each convolutional structural and content information. However, these methods are layer is equivalent to a first-order low-pass graph filter that only takes mostly limited to lowpass filtering and do not explicitly optimize the the most immediate neighbors of each node into account.

As a hot research topic, many multi-view clustering approaches are proposed over the past few years. Nevertheless, most existing algorithms merely take the consensus information among different views into consideration for clustering. Actually, it may hinder the multi-view clustering performance in real-life applications, since different views usually contain diverse statistic properties. To address this problem, we propose a novel Tensor-based Intrinsic Subspace Representation Learning (TISRL) for multi-view clustering in this paper. Concretely, the rank preserving decomposition is proposed firstly to effectively deal with the diverse statistic information contained in different views. Then, to achieve the intrinsic subspace representation, the tensor-singular value decomposition based low-rank tensor constraint is also utilized in our method. It can be seen that specific information contained in different views is fully investigated by the rank preserving decomposition, and the high-order correlations of multi-view data are also mined by the low-rank tensor constraint. The objective function can be optimized by an augmented Lagrangian multiplier based alternating direction minimization algorithm. Experimental results on nine common used real-world multi-view datasets illustrate the superiority of TISRL.

Although numerous algorithms have been proposed to solve the categorical data clustering problem, how to access the statistical significance of a set of categorical clusters remains unaddressed. To fulfill this void, we employ the likelihood ratio test to derive a test statistic that can serve as a significance-based objective function in categorical data clustering. Consequently, a new clustering algorithm is proposed in which the significance-based objective function is optimized via a Monte Carlo search procedure. As a by-product, we can further calculate an empirical $p$-value to assess the statistical significance of a set of clusters and develop an improved gap statistic for estimating the cluster number. Extensive experimental studies suggest that our method is able to achieve comparable performance to state-of-the-art categorical data clustering algorithms. Moreover, the effectiveness of such a significance-based formulation on statistical cluster validation and cluster number estimation is demonstrated through comprehensive empirical results.

Conformalized quantile regression is a procedure that inherits the advantages of conformal prediction and quantile regression. That is, we use quantile regression to estimate the true conditional quantile and then apply a conformal step on a calibration set to ensure marginal coverage. In this way, we get adaptive prediction intervals that account for heteroscedasticity. However, the aforementioned conformal step lacks adaptiveness as described in (Romano et al., 2019). To overcome this limitation, instead of applying a single conformal step after estimating conditional quantiles with quantile regression, we propose to cluster the explanatory variables weighted by their permutation importance with an optimized k-means and apply k conformal steps. To show that this improved version outperforms the classic version of conformalized quantile regression and is more adaptive to heteroscedasticity, we extensively compare the prediction intervals of both in open datasets.

Nuclear Magnetic Resonance (NMR) spectroscopy is an established technique in analytical chemistry. As a result of its rich structural and dynamic information content, it is particularly suitable for compound identification. However, a full elucidation may not always be possible or even necessary since some properties might be achievable directly from the spectra. If this is the case, a prioritisation of substances to be closely investigated for compound assignment can be done in the early stages of a study. A previous example for this idea was demonstrated in [1], where the authors showed that the existence of certain substructures can be concluded from profiles in the spectra. Another potentially useful application is chemical classification. These rely strongly on annotated chemical entities to provide a computable chemical taxonomy based on substructures.

The increasing reliance on online communities for healthcare information by patients and caregivers has led to the increase in the spread of misinformation, or subjective, anecdotal and inaccurate or non-specific recommendations, which, if acted on, could cause serious harm to the patients. Hence, there is an urgent need to connect users with accurate and tailored health information in a timely manner to prevent such harm. This paper proposes an innovative approach to suggesting reliable information to participants in online communities as they move through different stages in their disease or treatment. We hypothesize that patients with similar histories of disease progression or course of treatment would have similar information needs at comparable stages. Specifically, we pose the problem of predicting topic tags or keywords that describe the future information needs of users based on their profiles, traces of their online interactions within the community (past posts, replies) and the profiles and traces of online interactions of other users with similar profiles and similar traces of past interaction with the target users. The result is a variant of the collaborative information filtering or recommendation system tailored to the needs of users of online health communities. We report results of our experiments on an expert curated data set which demonstrate the superiority of the proposed approach over the state of the art baselines with respect to accurate and timely prediction of topic tags (and hence information sources of interest).